 unless we realize this. Hi everyone. Today is September 4th, 2019. It's a Wednesday and it's the second day that school that started in my part of the world. So in 2019-2020 school year. And for today's stream, we're doing what we title it. And I think that's the sort of format we're going to keep for all of school year for this year. We're calling it Drop in Math Touring Session 2019-2020, number one. Let's do some math open discussion. Welcome back. Hope you're all have fantastic, fantastic summer vacation. What I'm going to do, I'm just going to do a little bit of prep work down here while we wait for people to hop on the chat, hop on the stream. I'm just popping out the chat right now. And we're live streaming. And that's about it. We've done, we did a few of these last year. Like I forgot, I lost the number. I don't know how many we did. We started off in some, you know, a format where we're covering certain topics. And we might do that as well. We might just say, okay, for this stream, we're going to cover preliminary, preliminary grade 10 material or grade 11 or do some grade 12 material. And during exam times, we'll do review of grade 10, grade 9, grade 8, even elementary school. We'll do, we'll do different things. Last year was more open. I'm going to keep on doing these open live streams until we get some kind of structure going on. If people are okay with doing this format, we'll continue it. If people want specific topics or specific years covered, we'll do that. Okay. And that's about it. So we're just going to wait until people show up. And if you have questions, let us know. It is an open discussion. So in general, we do talk about math, science, biology, chemistry, different related material. But if a math question comes up, that takes precedence over everything else. Okay. That takes precedence over everything else. And one other thing earlier, well during the mid-summer, so I had a hardware crash. One of my hard drives, my main editing hard drive went boot. And in the last few weeks, I've sort of backed things up. I got access to it. I could read it and kind of write on it. So I got access to it. I backed stuff up. I transferred stuff to another hard drive, internal hard drive that I have and I'm going to start editing on. So edited videos should start coming sooner rather than later. Okay. One of the first things we're going to do is do a little personal finance, ASMR math stuff related. And we're selling some comic books on eBay right now. So I've created a spreadsheet where I've entered a lot of this data and how much we sold the stuff, you know, how much shipping was, how much eBay fees were, eBay shipping fees were, paypal fees were. If there are any refunds I have to do where I have to do one refund. It looked like the one comic I sent out anyway was damaged during shipping. I believe anyway. But either way, I did a partial refund. But everything else we've been selling. Everyone's been happy with it. They've been leaving positive feedback. I know some people have been grabbing some stuff because they want to support the work and whatnot. Let me actually do this here. These are, if you want to keep track, because we can definitely talk about do a little mathematics as these things get knocked out, right? So that would be super cool. Hey Casey, Starsky, how you guys doing? I was on my eBay page. There's stuff ending right now. Oh, you know what? That's the item. Let's see what I made. I think we want this. Let's see. Yeah, this is the shorter version. I think anyway. Here's the shorter version. Okay, that should do it. Sorry, good afternoon brother. How are you doing? Mathematics is back. I'm psyched for this year's math session. I got some distant learning education people. We're going to start these live streams from the get go right from the school beginning. So it would be cool to see if there's anyone coming in at the beginning of a school year and having questions related to content from a beginning of the school year and see how they progress. And I'm going to treat, hopefully I'll try to remember who's who and what type of questions are asking. Maybe they'll remind me. You know me and names. I'm very good with faces and situations and stuff like this. But names just throw me off, right? But hopefully we can keep track of how people are progressing and the way I'm going to treat it is the same way I treat the rest of my students, which is basically if they ask me a question, we'll try to answer that question. But we're going to be planting seeds for future years coming on, right? Because I want to prep them for higher grades, not specifically what they're asking, but what is to come. I find that to be the best way to teach mathematics both on lonely piggy. How are you doing? Bonjour, bonjour. Rick, John, Nova, what's going on? I was just watching the video you put out earlier. I really enjoyed your time. Thanks, brother. Thanks, Nova. Loving the patio yesterday. For those of you who might not know, we did an economics personal finance video yesterday on the patio. And it looks beautiful, really. That's one thing I love about doing the gardening and dealing with plants. All of a sudden, you can create a scenery, like just create an amazing space where you can just go sit there and stand there and go, this is nice. This is nice, right? I had one person, one person commented on the YouTube video, I think. It was in the bit shoot. It was a YouTube video. The bit shoot doesn't get very used right now, rather to YouTube. It's all commented on the YouTube that they thought the background was sort of a scene, sort of an image that I had put behind me. And then when I got up, they're like, whoa, what? That was a little negative. She told me, good, I need some chill vibes while doing homework. Nice, nice, nice. School just started. School just started. Fun. I'm watching some of these comic books sound. Some are going higher than what I expected. Some are going for lower than what I expected. It's crazy, like just to give you an example, because this is math related to a certain degree, right? The first appearance, I've got a whole lot of comics on eBay right now. They're ending while we're doing this live stream, right? So it's cool looking at it while we're just being here, right? But the first appearance of this character called Claytus Cassidy in Amazing Spider-Man 344 sold for $91. I think I want more. How much did I sell for? So the first appearance sold for $91, and it was in 9.6, 9.8 condition, which is very high grade, okay? The second appearance of this character is the origin sort of with the previous one, which is a little bit lower grade, 9.4 sold for $15, right? So looking at the differences between these things is brilliant to me. That's where mathematics for me, some of the stuff really kicks in, where you can start getting a feel for what's going on in sort of an economic front and demand and supply and hype and whatnot. It's amazing to me, right? Masks of Raven, how are you doing? Literally just a comic in the mail as your stream started. Nice, Captain America 290, first appearance of Mother Knight, which was Mother Knight. Hey, Chichuah's life, doing good lives. Thank you very much. Mother Knight, Mother Knight, Captain America 290. Reminder that it's September, everyone. Half price subscriptions, but Chichuah still gets the format. Oh really, cool. Thank you for the reminder, Casey. Great time to show support if you're able. Yeah, if you're able, fantastic. I would greatly appreciate it. I've had a few expenses pop up this summer. Daughter of, oh daughter of Red Skull is Mother Knight. Cool, nice buy. And that, depending on how they treat things, because they've been the comic book industry in a big way, Spider Beans, how are you doing? In a big way, they're pushing female characters. They have, they started about, basically 2010, 2012, 13, it really started kicking into gear where a lot of female characters were taking all the roles of previously male characters and daughters were coming up and stuff like this. And they're making their way into the Marvel Universe, right? So some of the comic books that people were like, oh man, I can't believe they're doing this, blah, blah, blah, blah, blah, they're fetching amazing prices, right, in terms of investing and stuff like this. So nice buy, because the odds are the daughter of Red Skull will make an appearance somewhere in the Marvel Universe, right, or Disney Universe, and even bet your bottom that people are going to be chasing it. You're going to be chasing it, right? It's crazy, it's an amazing industry, so cool. I had a friend over recently, just the last few days, and he plays in markets and stuff like this, and I showed him what I was doing, and he's like, oh, so it's like stocks? I go, yeah, it's just like stocks, right? There is storage fee, if you want to think about it that way, that you're taking on, but there's also entertainment value that you're taking on. I just bought a 9.6 CGC of Mycronauts for $5, oh dude, that's a great price, yesterday too, first ever slab, yeah, and that's a great price, like just getting a CGC would have been my part of the world, it costs like $35, $40 Canadian, oh yeah, you're talking US dollars too, so I don't know if that's a great price, sounds like a great price to me. I've seen some slab stuff, CGC stuff, of comics that people aren't chasing, they're just randoms, go for like $5, I've seen CGC 9.8 go for $5, shipping would have been like $20, so $25 you get a CGC 9.8, and there was a few of them that went for 10, 15 in the teens, so if you combine shipping, you're actually buying down the pipeline CGC book for less than what would cost you to send one in if you knew it was that great, it's interesting, as you can tell, I'm very excited about crunching these numbers that we've gotten off eBay, we've gotten, we've been selling books on eBay for about two months now, so far, after today and tomorrow session we were sold around 80 bucks, right, so if we sold around 80 bucks, then that's a pretty good number, we can start doing some crunching and start trying to get a feel for what the expenses are, what the ratios are, what the return on profit might be, and what all the fees are, stuff like this, I've got my spreadsheet, big spreadsheet of different columns going on, I love spreadsheet data, right, mathematics, mathematics, initially I wasn't even going to start these math lifestreams until end of September, because that's when things start kicking in, but because I was looking at the data I'm like, let's do math, let's get going, let's start it up, this is me rambling on by the way for like 15 minutes, and keep in mind if you have any math questions, ask away and try to address any issues you might be having, right, the big book today that's going to be selling is Amazing Spider-Man 361, right, the first big book sold which was 344, which was the first appearance of Tata's, 361 is big as well, huge in the comic book realm, who's starting, is there anyone from high school here, or is everybody in college, university, or just chilling, by the way, I picked some blackberries yesterday, I'm cooking, I'm making blackberry jam right now in segments, this morning I had two pots going, I had 15 pounds of blackberries, yeah 15 pounds of blackberries cooking today, so I had two pots going, I've reduced them, the next step, so when I'm doing this I just turn it off, I put it on the side, you can do that with jam, right, you don't have to continue the whole series in one shot, right, so I have two pots sitting and then I'm going down the stream, I'm going to go and mill them and cook them up and then draw them, right, thank you, are you a professor, no, no, no, I ended my academic career soon after getting my bachelors in geophysics and mathematics, if x squared plus 5x plus a equals x plus b squared, what is a and b, a and b, so that's when you're doing that, you're assuming it's a perfect square, so if you're assuming it's a perfect square, so unfortunately that one doesn't work out evenly easily for us, right, so let's do these, by the way this is the beginning of the year, even for me it takes a little bit of time to get back into the groove of mathematics, because what you'll notice, what every educator, every teacher, every parent, every student notices, anyone that's going in school knows this, that deals with the school system knows this, when you come back after summer break you've forgotten a lot of stuff, right, or it's in the back burner you need reminders and it takes a little bit of time to get back into the groove, right, so masquerade, let's check this out, x squared plus 5x plus a, x squared plus 5x plus a is equal to x minus or plus, plus b, plus b squared, right, so this is a simple trinomial, this guy, this is called a simple trinomial, try means three terms, right, first term, second term, third term, and terms are separated by plus and minus, right, so whenever you have plus and minus between x terms, right, that's what you call trinomial and nominal is derived from polynomial, polynomial, okay, and what is a polynomial, polynomial is a function, I'm having trouble simplifying compound, compound fractional expression, you want to simplify it here, let me write this down, yours will be perps, I think yours should be easier than masquerade, because that's not a perfect square, but I'm going to go through a whole process of explaining what a perfect square is, do a simple one, and then we'll try to get the answer for this one, right, I'm still thinking about it, so x plus 1 over x plus 2 plus, okay, so the way you've written it, brackets are your friend, friend, okay, so you wrote this like this, 1 divided by x plus 2 divided by x, right, so my question to you is, is this this divided by x, where this guy is in the top, or is this this 1 over x plus 2 over x, which one is it, does it make a difference, let's see if it makes a difference, right, the first one should be easy, because the x squared will cancel when you expand, x squared will cancel when you expand, yeah, I mean you can do this, here, this one, you expand this and you put it in the same form, okay, hold on a second, while we're waiting for this answer, it might not matter, but because you wrote it out this way, I need you to express it properly, right, so if you expand this, this guy, x plus b squared is equal to x plus b times x plus b, right, x squared if you expand this becomes plus x bx plus bx plus b squared, right, because you go this times this times this, that's foiling, right, combine these two guys, you're going to get bx plus bx is 2bx, 2bx, right, so what we have right now is we've got a trinomial equals a trinomial, easy peasy, right, because this guy, we'll rewrite it up here, x squared plus 5x plus a has to equal x squared plus 2bx plus b squared, so this is three terms, this is three terms, right, they're both three terms, so if I, for example, if I give you this, 2 to the power of x is equal to 2 to the power of 3, what's x, what's x, 2 to the power of x is equal to 2 to the power of 3, this is something that comes up and sometimes I ask grade 12s this because this peaks his head when you're dealing with logarithms, exponential logarithmic functions which is a grade 12, right, you got 2 to the power of x is equal to 2 to the power of 3, x has to be 3, this is like a place marker, right, if this whole thing is equal to this whole thing that's a 2 and that's a 2 then that has to be a 3, so x is equal to 3, there's no choice, right, this is the same deal, x squared equals x squared, so we're okay there, 5x has to equal positive, that should be including the sign in front of the number, sorry if I'm not reading any of the chat I'm just gonna cover this up, so positive 5x has to equal positive 2bx, right, so 5x is equal to 2bx, you divide by x, right, take both of those out and then b is equal to 5 over 2, right, if b is equal to 5 over 2 then b squared is 25 over 4, right and a has to equal b squared, so a is equal to 5 over 2, right, because what you're going to do is going to say positive a has to equal positive b squared, so a has to equal b squared, but what was b? b was 5 over 2, right, so b is equal to, so a is going to be 5 over 2 squared which is 25 over 4 and a is 25 over 4, sorry the other way around, a is 25 over 4 and b is 5 over 2, right, it's just place markers, the first one on the top left, the first one on the top left, the first one on the top left, maybe oh your left that's right, it's your left it's my right and the first one on the top left, okay we'll deal with it like now, that will be negative, my problem when doing my column jazz is I get the hang of solving a set of problems, then it seems like the next step set has completely different rules for how to solve it, the rules of mathematics don't change, you shouldn't think of it as different rules of solving it, you should think about it as a different process, it's an easier way to solve it, right, like the rules keep changing and I'm just supposed to know why, here's the thing that again that one I get, it's not the rules that are changing, it's the method you go about solving the problem is changing because the rules of mathematics are the same, right, it's just based on five axioms, right, so adding is adding, subtracting is subtracting, there's rules associated with adding, subtracting, multiplying, dividing, the equals sign, right, as long as you know how to add, subtract, multiply, divide, move around, equal sign, you can do almost anything you want, right, the rest of mathematics, the rest of mathematics to large degree is conceptual, is taking that and applying it in the real world or applying it to a data set or applying it to a function, I could be exaggerating here a little bit, there might be mathematicians, I think Master Riva is pretty good at math, so you might be going, Chicho, stop saying that, right, but I'm generalizing and simplifying it, right, it's not the rules that change as you approach to solving the problem that changes and that comes with practice, right, that comes with understanding the problem, not trying to memorize how to solve the problem but understanding what the problem is asking you, you know Chicho, we love your stuff for a long time, keep it up man, but we'll do sneaky, sneaky wall versus zero, let's do this one, okay, so we're trying to simplify this, let me find the original and then one over x and then plus two and I'm assuming the plus two is like this, is everyone okay with this one, I hope everyone's okay with this one, I was going to take it down a different route show you how you factor a perfect polynomial, you couldn't factor that, so you have to expand that and link it up, but we'll skip that I guess, right, we went to that, did a mean of it right away, so let's do the question perps is asking, so we got x plus and then this guy, right, yeah, so one over x plus two over x and then we got minus one over x, minus one over x plus two, I'm assuming it's like that, I'm assuming, yeah you put a space between them, right, I'm assuming this one is not supposed to be this because you put a space between these guys when you typed it, right, so how do we approach that, we just want to simplify this, right, sneaky wall versus zero, thank you for the tier one sub on a, what's it called, KC, it was called September, September day, everyone, September month, everyone I guess, let's check this out, simplify, yeah, so how do we go about this, well I would take care of this first, there's multiple ways of doing this by the way, right, but I would take care of this guy first because this is the ugliest one, right, so what you want to do is take care of the other guys first, so I'm going to take this, you can do it on the side in general and whenever you've got problems where you're going to be doing multiple steps going down, right, because we put out a video where we said recognize the pattern, right, you sort of want to simplify it going like this, right, at least I could do for the little years of peaceful sleep and relaxation you're talking about, my pleasure man, I hope you didn't have too many chicho dreams teaching you mathematics, thanks chicho, that makes more sense to me now, then you'll see that is not the spoon that bends, it is only for yourself to not try to bend the spoon, so let's do this one on the side, right, take this guy and let's simplify it here, right, so this whenever you get fractions or couple fractions, right, write them on sideways as a division statement, right, so you can do it here, we'll do it here because I don't think this is going to take all the way down here, so you can go like this, 1 over x plus 2 divided by x, and that what that means is 1 over x plus 2 division change the multiplication flip the number term variable after expression, right, and you flip this it becomes times 1 over x, so the bottom here is 1 over x plus 2 times x, right, makes sense, so this guy is really that guy, so this now becomes x plus 1 over x plus 2 times x, minus 1 over x plus 2, now depending what grade you're in, okay, because you get this in grade 10 in my part of world, you also get it grade 11 and 12, if you're in grade 10 you don't have to worry about this one thing, but we're going to do it because we're laying out a foundation for grade 11 and 12, right, whenever you get fractions with variables in them, okay, the thing you always have to do on the side is note your restrictions, okay, thank you for the follow, I couldn't read both bottom here, right, you have to make a note of your restrictions, okay, so so what we do is the restriction we have in mathematics, okay, is no dividing by zero, right, we can't divide by zero in mathematics, we've talked about this, right, 1 over zero is undefined, you can't divide by zero, if you want me to go over that let me go over down here, I'm assuming everybody appreciates that right now, they know why, right, but because we can't divide by zero in mathematics, whenever you get a fraction with variables in it and variables just mean things that can vary, you have to put restrictions on that variable because it can vary, right, I hope that makes sense, right, 1 over x, x can be almost anything, there's only one thing really that x can't be, what can't x be here, well the denominator can never be zero, so whenever you get something like this, take the denominator and say x cannot equal zero, that was easy because the denominator was x, over here this is a complete fraction as well, so again x can't be zero, over here this is a fraction within a fraction, so we have another fraction here, so take the denominator for this fraction and say x plus 2 cannot equal zero and you bring the 2 over so x cannot equal negative 2, so we have two restrictions, if you had other fractions with variables in the denominator, you would do it for every single one, right, so for example if we have another one here saying plus 1 over 3x minus 1, you would say 3x minus 1 cannot equal zero, solve for this, you get x cannot equal 1 over 3, 1 over 3, right, so for any fraction where you have a variable in the denominator, you write down your restrictions, okay, this wasn't in there, so we're going to keep that out, and by the way the reason you're doing this is because in general, you're talking about functions, right, you're talking about a mathematical expression that relates to a world situation or something imagined, right, something you want to analyze and whatever it is, whatever system you're looking at, you have to know what your restrictions are, you really do, right, because every system has restrictions, limitations, okay, and for this system, our restrictions, our limitations is x cannot equal zero and x cannot equal negative 2, so we should have done this up here, right, in the first step before we proceed crunching anything, okay, and keep this in mind, in the crunching process if you end up getting additional fractions with things in the denominator, then those cannot equal zero as well, okay, so sort of continues, you always have to keep an eye on it, so now we want to simplify this, whatever you want to simplify this, this is just adding fractions, right, if I told you what's 2 plus 5 over 3 plus 1 over 7, you would say oh, I'm adding fractions, I'm going to write 2 as 2 over 1 because everything can be over 1, it's a fraction, and what do you do when you're adding fractions or you're looking for a common denominator, what's the common denominator between 1, 3 and 7, 21, right, and then you ask yourself would you multiply 1 to be 21 and multiply it by 21, so 21 times 2 is 42 plus multiply 3 by 7 to get 21, so you multiply 5 by 7 which is 5 times 7 is 35 plus multiply 3 by a 7 by 3 to get 21, so multiply the top by 3, you get plus 3, and by the way the reason we're allowed to do this is because we're not changing the value, the weight of this expression, all we're doing is we're making it look different, how are we making it look different, we're making it to become one expression where they have a common denominator, right, so the only number that we can multiply anything by without changing its weight, its value is 1, right, so we're really multiplying this number by 1, this number by 1, this number by 1, but because we want to make all three of them look different, we're choosing what this one looks like, this one here is 21 over 21, we're multiplying this expression by 21 over 21 because that way it puts them under the same denominator, this one we're multiplying by 7 over 7, this one we're multiplying by 3 over 3, right, now keep in mind we're not multiplying each one of these by different numbers, we're multiplying them all by 1, 1, 1, 1, but the one looks different for each one because they had a different denominator and we're trying to bring them all up, raise them all up to the same common denominator and you can't multiply anything by other than 1 if you want to keep the value the same, right, so if you multiply the bottom by 21 then we have to multiply the top by 21, bottom by 7, top by 7, bottom by 3, top by 3, the weight of this expression hasn't changed and it looks different then you can add all this up, right, so what are we, 2 plus 3 is 5, 5 plus 5 is 0, put a 1 up here so that's 80 over 21, right, 77 plus 3 is 80 over 21, 80 over 21 is the same as this, right, but this is cleaner, this is what we're hoping to do with this, make it look cleaner, right, more condensed, simpler, let's do it, what we did here is exactly what we're going to do here, but they just happen to have very close, so let's convert them all to fractions, you don't need to necessarily do this every time, but you can if you're starting out, that's a fraction, that's a fraction, over 1 over 1, 2 over 1 is the same thing as 2, right, so just put them all as fractions, that way visually it looks like we're dealing with fractions, right, and then you ask yourself what's the common denominator, well we need a 1, 1 is a 1, 1 can be anywhere, if I write down 2, I could write down 2 over 1 times 1 divided by 1, that's still just 2, so 1 you could put anywhere, right, so we don't have to worry about the 1, we need an x plus 2, and we need an x, here's another x, but if we have an x here, x is already covered, if this was x squared, then we would need another x, so we would need an x squared, not just an x, because an x squared covers x, but an x doesn't cover an x squared, we need another x, right, but this isn't an x squared, it's just an x, and then a 1, so common denominator is x plus 2 times x, if that's the case, then what do we multiply this guy by to give us x plus 2 times x, we multiply it by x plus 2 times x, so we're going to multiply top by x plus 2 times x, right, I hope I can write this in one go, well that's good, so this becomes x times x plus 2 times x plus, and you can simplify it out here, we'll do it right down the step here as well, x plus 2 times x, so this x times x is x squared, right, and then x squared, you can multiply that and you would, for these types of things you multiply them all because you could combine like terms at the end most likely in the top, that's why you could compress them, right, we added 42, 35, and 2, 3, 3 to get 80, right, so over here that's going to be x times x is x squared, and then you multiply the x squared inside, so that becomes x cubed plus 2x squared, this guy, we just multiplied by 1 to give us x plus 2 times x, we didn't change it, apologies for the things not focusing right away, right, it's all weight, so my camera freaks out a little bit, so that just becomes plus 1 because we don't have to multiply that by anything, that is that thing, right, minus, what do we multiply x by to give us x plus 2 times x, we multiply it by x plus 2, okay, now whenever you simplify these types of expressions, whenever you have a negative sign, whatever comes after a negative sign when you're expanding it, put it in brackets, because that negative sign is going to affect everything inside the brackets, correct, so what do we multiply x by to give us x plus 2 times x, we multiply it by x plus 2, right, so it's going to be 1 times x plus 2, and over here, what do we multiply 1 by to give us x plus 2 times x, well we multiply it by x plus 2 times x, so it's going to be 2 times x plus 2 times x, okay, let me move these over here, our restrictions were, I usually go right like this, restriction x cannot equal 0, and x cannot equal negative 2, okay, which really doesn't matter to us right now because this doesn't equal anything, okay, let me kill this because we're going to need the space, side waves, let's make them negative 2, negative 2, so it shows more clearly, hey trepid, how are you doing, hey chicho, long time, no see, hope everything is well, everything is well, school year started, I'm all excited, as if you can't tell, speedy Gonzalez, I'm like yeah, yeah, let's go through this, so what do we multiply 1 by to give you x plus 2 times x, we multiply it by x plus 2 times x, so that's going to be 2 times x plus 2 times x, okay, let's simplify these things, because we simplified this one already, that one doesn't simplify, it's plus 1, negative 1 multiplies in, now you don't need to put the negative there, I never do, we're doing it for what's it called, ah I want to erase it, you can if you want, have students that do that, but you don't need to, 1 is a 1, so if you have a negative here, there's a 1 in front of 2, there's a 1 in front of 2, so that's going to be minus x minus 2, and then we're going to multiply these guys together, multiplication doesn't matter which order you do it in, the 1 is imaginary, the 1 is imaginary, perfect, thank you perps, the 1 is imaginary, it's not a imaginary number like complex numbers, square root of negative 1 or anything like this, it's just you imagine is there, it's a placeholder, now multiplication, some people make the mistake thinking that they have to multiply in order, you don't, for example 2 times 3 times 4 is the same thing as 2 times 4 times 3 is the same thing as 3 times 2 times 4, right, 6, 6 times 4 is 24, 8, 8 times 3 is 24, 6, 6 times 4 is 24, right, multiplication order doesn't matter, as long as there's no plus and minus between things, right, so we've got three things multiplied together, I'm going to multiply these two together first, 2 times x is 2x, and then 2x multiplies this in this, 2x times x is going to be plus 2x squared, 2x times 2 is going to be plus 4x, the last step you need to do in this is simplify this expression, combine like terms, and the way I do it, I scan this thing and I combine the highest powers first, right, so I've got an x cubed, there's no other x cubed, so this is x plus 2 times, there is no other x cubed, so it's just x cubed, you've got a positive 2x squared, so we're going to combine it with other x squares, right, here's a positive 2x squared, so 2x squared plus 2x squared is 4x squared, plus 4x squared, we've got a number 1, and we've got a negative 2, and that's it for the numbers, right, but I'm not going to write that here right now, because I want to have it as descending order, and I know there's another x here, so I'm going to triangle this, so I know to combine it with this, right, so the two circles I've got to combine, and the two triangles I have to combine, let's do the triangles first, negative x plus 4x is positive 3x, 1 plus 2x, oh sorry, 1 minus 2 is going to be negative 1, you want to express your final answer in descending order in general, so this guy simplified this ugly looking thing really, it really is ugly, it's not really ugly, like all visual, mathematics stuff, but it's it's messy maybe, right, you can express this like this, and in general you leave that alone, you don't multiply that in, okay, the only reason we multiply all these in is because things are going to combine to simplify it further, that simplified is this, that's a nice expression I like it, it looks pretty condensed, things are descending, I hope that helped, sweet thanks to Joe, my pleasure, this is the most complicated question I've had so far this year, the year just started yesterday, I haven't started working with my grade 12s yet, I only started working with elementary school students so far, like one high school as well, a couple high school, early on there's a kombucha, I got a kombucha going, a little bit of dark chocolate going, I might do some random random other streams in the next today and tomorrow, we'll see, we have a barbecue going on tomorrow, we're gonna do a lot of prep food prepping today, I don't think I'm gonna have time to livestream because I'm also cooking making blackberry jam, so today I'm making blackberry jam, prepping marinating meat for barbecue tomorrow, tomorrow I'm gonna do a full-on barbecue, cooking up a lot of shish kebabs, oh, somebody erased this, the great thing with the video is you can just go back and pause it and copy it all down if you need to, take your screenshot and look at what else sold is the comic book from, let's take a look, we could do some mathematics on that stuff right now, three more sold, let's check it out, 35, wow, wow, wow, so amazing spider man, let me give you the prices on them so far, amazing spider man, 344 sold for 96, that went above what I thought it was gonna go, but that thing started kicking up and price baked on last year, a year ago you could have bought this thing for 10 bucks, amazing spider man, 345 sold for 15, that was a deal and a half, the 344, that's a going price now, 346, these are like going prices, this is the first time, I didn't know this, I looked this up afterwards, amazing spider man 346 is actually the first time you see Venom's tongue like this, so it's the first appearance really of the Venom tongue in this format, I believe, and it's Eric Larson doing it, and the green gook, and the green gook I believe is the byproduct of Venom eating, right, it's residue poop, and then amazing spider man 347 sold for 38, amazing spider man 351 sold for 35, and 360 sold for 34, oh and all these are going to the same buyer, oh no no, the 344 went to someone else, and the person has been buying a few of these amazing spider man, you can crunch these numbers, the crazy thing, the 360, amazing spider man, sorry, amazing spider man 359 and 360, a couple of years ago you could have bought them for less than ten dollars, right, because of the Venom movies coming out and whatnot, they've kicked up in value big time, big time, I don't know what their going rate is really right now, I think that's fair value for them, if log AX equals K, what is log square, I'm assuming you shouldn't have a bracket between those, where, oh that's the base, is that supposed to be the base, that's supposed to be the base, so let me write this down, I'm assuming this is what you're writing, log AX, if log AX is equal to K, right, is log, what is log, log square root of AX equal to K, right, so how do we do this, we think about this, so basically we want to find out what A is, we want to do, we want to find this box, you're kicking me straight into grade 12, log, think about this, what's the best way of approaching this, we could figure out what A is, sometimes when you're doing mathematics, the best thing to do is is just start messing around with it, I lost the chat, so I'm just going to start messing around with it until we get to the right approach of solving this thing, so we'll find out what that is, oh we can do this, check this out, the best way to approach this is this, right, so there's a rule in logs where it says log, log AB, right, can be written as log B over log A, with whatever base you want here, and usually you just leave it as base 10 and you don't bother writing the base 10 here, let me write this a little bigger, hopefully we're not gonna, I think I need to stand in front of the whiteboard a little bit for the camera not to go out of, thank you, so the rule in log, let's write it up here, there's a rule in log that says log AB, and A and B can be anything, if you want we can use X and Y, so we don't get confused with, well not X and Y, let's go M and M, because we don't have M and M here, right, so M and M can be written as log whatever base you want as long as it's the same M over log box M, and those have to be the same, but if they have to be the same in general we'll put another variable in there, right, let's call it Z, I don't know if this is name convention proper or not, usually M and M use for the base actually, whatever, I'm gonna call this Z, Z and Z, that means they have to be the same, so basically it's telling you if you got log X over square root of A, this guy you can write as, I'm just gonna simplify in this direction, log X over log square root of A, right, that is that, now there's another rule in logs that says this, here we'll do the exponent rule first, right, because this is a layer, by the time you get to here, there's the assumption rightfully so that you should know how to deal with powers and radicals, right, exponents and radicals, and we've got a whole series of exponents and radicals, we've talked a lot about this, if you check out the YouTube playlist for the math videos, I believe we did this in series two back in 2009, and this has come up over the years multiple times in other language and mathematics videos we've done or ASMR math videos we've done, I think we actually have a one long ASMR math video we've talked about, exponents and radicals, right, and these are radicals, so radical rule says this, square root of something is really A to the power of a half, right, all you do if you have the root of anything, let's call it Mn, there let's use Mn again, right, let's erase this and do it this way, the M root of N can be written at N to the power of 1 over M, the M here just goes in the denominator in the power, right, so this guy we can write as log X over log A to the power of a half, okay, so that's not a log rule, that's an exponent rule, now there's a log rule that says this, log rule says log of N to the power of M can be written as M log N, so if you have a log of anything to a power that power can be brought down to the front, makes sense, so we can grab this guy and bring it to the front, so this can be written as log X over 1 half log A, 1 half, so what this really means is I want to kick this up here because we don't need any more log rules, do we need any more log rules, if we do, I'll leave a little blank here just in case there's another log rule that we have that we might need during the simplifying process, but from here, here I'll go down one more here, from here we could write this as this, there's an imaginary one here, right, now making this a little bit more complicated than it really is just to put in the the extra steps in there so you see what's going on in terms of the flow of logic, right, so this is 1 over 1 over 2 and this is log X over log 8, right, 1 over 1 over 2, yeah we'll use this space here, 1 divided by 1 over 2, let's just 2, but let me show you, right, whenever you have, it's like the previous question, whenever you have fractions on top of fractions, do it sideways, lay it outside, so 1 divided by 1 over 2 is really 1 times 2 over 1 which is just 2, so this guy becomes 2 times log X over log, can you, do you know the answer right now, it's only or once, two steps away if you want to do every step, right, we basically finish the problem, right, but you have to finish it, you have to lay it down, right, if you take a look at this where do we see this, is there, here's the log rows, this is a log row, right, and this is a log row, okay, that was an exponent row and that's just the division row and I'm calling these masquerades, right, and I'm just, I'm calling these rules, but they're not rules, they're just things that the language of mathematics says needs to be because that's what the symbols, the expressions tell you to do, right, like a period in the sentence tells you the sentence has ended, the next letter in the sentence has to be capital, okay, and then you can start the next thought or whatever it is you're starting, right, comma means something, colon means something, that's what these things mean, now if you take a look at this, log X over log A, well that's this rule here, but going in this direction, because the rules of mathematics, if you can go this way you can go the other way, right, they're bi-directional, is that what we call it, complementary, whatever it is, right, these go both ways, these go both ways, so if you have a number in front of log, this guy can go up top as well, right, well this guy is log of M over log of N, M, X, and A, and that just becomes that, so this guy becomes to log base A of X, what's log base A of X, well log base A of X is K, so this just becomes 2K, fun, fun, so would there be a general rule that for a log base to a power you can just multiply the log by the inverse of the power, you know what, for me, masquerade even, there probably is, but I don't encounter these types of problems often enough to try to remember what they are, right, so for example what if this was cubed here, then you got to actually multiply it by 2 over 3, I don't want to memorize it, I know the process of how to get the answer, right, so I just go through the process, if you were doing this, and here's the kicker, always keep this in mind, all those shortcuts that they teach you in school, use those shortcuts if you have, and learn those shortcuts if you have 50 of the same questions that they're going to ask you, if you're going to encounter one of these questions in one exam, right, it's not worthwhile trying to remember how it works, because if you have a misfire, right, we're human beings, if you have a misfire during the day of the exam, right, your neurons aren't firing at full capacity, you had something happen, bad day, you didn't have the right food the day before you ate the wrong food or drank the wrong drink, you might not be functioning at 100% capacity for an important exam, right, then your memory is the first place that fails you, right, knowing how to do something stays with you, right, really, it stays with you, so if you know the process involved in simplifying or answering this type of question, you don't have to memorize anything, special cases, you just go crunch, crunch, crunch, crunch, crunch, right, like for me, really, masker raven, who asked this question, was it masker raven, yeah masker raven, for me, even the previous question, even the quadratic question, the first question they asked masker raven, right, for me, when I see a question, in general, unless at the beginning of years anyway, when I start, when the school years start, in general, my neurons don't fire right away, and I know the answer right away, or I know how to approach the answer right away, I write it down, I take a look, I go, exactly what we did, what's the best way of doing this, just looks simple enough, but the square root is, the square root, right, oh man, I gotta deal with the square root, and then you go, oh, there's, this is about logs, so what are the log rules, so I get my memory, my mind to, so first thing is doing is sorting through the data, sorting through the visual that I see, right, and then the next thing I do, once I figure out what section I'm in, or what type of process I'm talking about, what type of system we're involved in, then I get my memory to access that database, right, and the database is the rules of the logs, that's all I really need to know, right, and all of these have derivations and stuff like this, but I could probably derive like two or three of the rules of logs, there's like eight of them or something, the other ones I would have to sit there and think, and like, oh man, I just know what works, I'm not gonna bother trying to do it, or I wouldn't look it up, right, and then what I do with my memory, I access these rules, okay, which rules apply here, well this is a log of something to different bases, so let's separate these, so you separate them, and then you separate them, you go okay, what else can I do, oh I still have this radical here, I don't want to deal with the radical, oh radical, that's just an exponent, so you kick it up to the exponent, you go oh, logs has a rule for exponents, which is if you guys log of something to an exponent, you can kick it down, oh let's do that, oh nice, look at this, that guy is really that guy, oh nice, so all I gotta do is just deal with this guy, and that's just fractions, sometimes I fail, I write down a problem and I go, I can't remember how to do this, if I don't, I move on, but I keep this in mind, maybe later on with some of the problems that you're dealing with, all of a sudden you remember the approach you need to take to be able to solve this type of problem, okay, it's really beauty of mathematics is, it's not about memorization, beauty of mathematics is you just gotta just chill with it, right, they suck, great things, great things, how are you doing, hope you're having a great, great Wednesday afternoon, right, I haven't had time to go pick up my comic books today, I haven't had time to pick up my comic books today, hey let's see, did we solve, oh we solved two more, let's see what else we solved, this data set is going in, oh wow amazing spider man, so amazing spider man 361 went for 167, and this thing's been kicking up in price, really, in the last, the last one we solved which was one grade lower, well it was the same grade as this, went for 102, this one went for 167, okay, and during the last three months amazing spider man 361 has been kicking up in price big time, really, it's been kicking up in price big time, in the last year it's been going up through the roof, and all of this is because for the Venom movie, okay, not just because of that, the Venom movie really kicks things up, but carnage is an amazing character, some people will consider it to be the best villain in the Marvel universe, okay, greatest villain in the Marvel universe, the other reason is they had, at the end of the Venom movie, they had, what's the actor's name, oh I forgot the actor's name, he does an appearance as Cleatus Cassidy, we're not sure if that movie is going to go through, because Disney and Sony have separated parted ways in regards to spider man, but I don't know if Sony holds the rights to make Venom carnage movies, or Disney has the right to make Venom carnage movies, maybe it's shared, right, but we're going to see a lot more of carnage, hopefully, there's a lot of carnage fans out there going, man, we want to see more carnage, we want to see more carnage, very exciting, amazing time to be part of the comic book industry, and there was actually a reseller that was bidding the amazing spider man 361 higher and higher, they wanted to get their hands on this, this is a pretty sweet book, this is a pretty nice book, oh yeah, they were kicking it up, I'm glad the person that got it, got it, that's a given, okay, because they've been waiting for this one, there was a couple people waiting for these actually, so I'm glad at least one of the people that was trying to get these got them, really, that's good, that's good, fun, got the love man, when we start crunching these numbers, I don't know how deep we're going to go into it, but we might go pretty deep, depends on, I might do a short video on it first, because I'm just getting back into the editing videos with the new hard drive, well not the new hard drive, the older hard drive that I just used as backup, that hasn't had too much reading right on it, so that should last us a while, hopefully, at some point I'm going to do a serious upgrade, really, we'll go through the whole process, we'll make ASMR videos and share as much as we can what we're setting up and how we're going to go about doing this stuff, and we're going to get a bigger whiteboard to do, to do a little large mathematics, all right, I'm going to take this down, I'm going to take this down, by the way, a mask of Raven, I'm glad you were kept on asking about when we're going to start mathematics, I'm glad we started as sooner than later, I'm loving this, awesome, awesome, I'm going to grab a seat at the school for now, I'm going to get more math questions coming in, hopefully that wasn't too loud for you guys, sorry about that, I'm squished in here a little bit, are people in school right now, yeah, some people are just getting off school I guess, yeah, I actually set this up during what do you call it, school time, right, so I guess we'll have to start setting up, setting these things up later in the evening where people that are going to school, high school specific, high school elementary school, I'm assuming there's in 20 elementary school people here, but on Twitch anyway, but people who are taking high school math or college or university, as long as it's basic non-calculus related, you know, we can deal with it, so do it later on in the evening, so they'll be out of school, maybe start doing these things on the weekends, because that way we can't do any days that way if people need to work, need to be free to be able to pop in and do little mathematics, I just got home from first day of university, nice, first day of university, what a trip that is, seriously, nice, first day of university, I remember my first day, do I remember my first day, I don't know, I did, I did three rounds, I did one university and I went to a college and I went to a different university, and through each one it was in a different state of mind, right, so which university are you in, Masquerade, by the way, are you in the States or Canada or, I think you're in the States, well, first day of third year, but restarting with a new degree, oh, what are you going into, if you're going to mathematics, you got to start doing some tuition, Ottawa, University of Ottawa, Ottawa, I've been there, interesting town, I did some work there, I did some geophysics there, mathematics, of course, awesome, your future is bright brother, your future is bright, and basically in about a few months you're going to know more, you'll be able to teach us a lot of mathematics, really, you must be taking calculus, discrete mathematics, the UDN algebra, and most likely it stats as well, I'm assuming, one year, one year in university to be able to get my math minor, I took four math courses, right, in one term, and one of them I had no room to take because I didn't have to prerequisite for it, it was applied mathematics, second year, but in the second term that they offered, so was the advanced version, without a doubt, my hardest term in university that blew away all the other terms, really, like it was three times more work than all the other terms where I was taking either five or six courses, sometimes four, usually five courses average, right, I took four math courses, and I was doing at least twice as more work, two, three, four times more work, that was a load, that was a heavy duty, heavy duty, I had, what did I have, I can't remember what I had, I had applied mathematics, statistics, I got second year calc, I believe, yeah, second year calc, applied mathematics, statistics, I didn't take the linear algebra until the following year, so I can't remember, mathematics, you could go in any direction you want, which direction do you want to go in math, what are you interested in, computer engineering, electrical engineering, heavy, heavy mathematics, right, heavy mathematics, business is just straight up math, really, and some understanding of how the system is, where the loopholes in the system are, right, if you're willing to play the game, profits, got another one to go, what was the last one, yeah, wow, amazing span, about 363, went for 51, one was kicking it up, some of these things are going for heavier prices, man, this carnage is getting some serious, I've been tracking this as well, just to see what was going on, right, and it's incredible how fast the market is moving right now, it's incredible, really, and not just on the comic book front, on the stock market, on the crypto front, like cryptocurrencies right now, bitcoin, really, this is, if you appreciate this, and ask it really, the dream is pure math, but that's a long shot, I'm thinking, compside or stats might be more secure and fun, yeah, stats, computer science would be fun, if, well, I don't know, all of it could be very interesting, depending on which branch you go down, right, pure mathematics is a world on its own, right, it could be a lonely place, I think, and it could be filled with tremendous amount of challenges, I've known people on pure mathematics, and once they got to their degree in pure mathematics, they had a choice, their bachelor's degree in pure mathematics, they could have gone in the direction of getting their masters and PhD in pure mathematics, and they would, or they had a choice of going to electrical engineering, and they had offers from both realms, this one person, and after thinking about it for a while, they went into the realm of electrical engineering, and they did like it, but there was more politics involved in pure mathematics, it was, there was a certain amount of peace and brilliance involved in it, I don't know enough math, you know, for sure, yeah, masquerade, yeah, at some point, brother, at some point, I would love to go back to university and start learning, or teach myself, right, start learning more at mass mathematics, and I've told myself, I'm going to do that once I finish all the content that I want to create for high school mathematics, right, because after that, the only logical choice for me would be, if I want to continue this, and I do, I can't see myself not wanting to, it would be for me to go back and relearn the mathematics that I knew at university, which is my math, not it's good that way, right, and that will, and while I'm learning it, create videos and content to teach it, because I'm hoping a lot of that stuff will be triggered again, right, I'll remember the things, and I have all most of the books here, all the books here that I use, and then continue my studies, right, I would love to get into coding and learn certain things about solving codes and security, explore prime numbers, a little bit, discrete mathematics, and just communication, secure communication, both on a personal level, as a, anyways, a long story, as well as on a political economic front, because I believe in the mantra right now, in the realm of, well, whatever you want to call it, the mantra that has been said, that security, privacy, freedom, liberty should not be something that is brought into law, it shouldn't be something that is given to us from the top down, it should be by design, and the only way that stuff can be made by design is through the realm of mathematics, right, so if you have the right code, right mathematics, when you're rolling out forms of communication, transactions, just being and interacting within our societies, if you have by design, privacy and liberty in there, then no centralized power can ever take that away from you, right, that's my thing, I don't know if I'll ever get there, but I like talking about it, I like talking about it, and I'll wait, there's a long way for me to go to get there yet, right, but I'm going to try to push as many people in that direction as possible, mathematics, teach as much math as you can, right, teach as much as much math as you can, for me anyway, you got me all excited talking about math, yeah, wait to put these numbers in a spreadsheet, do you use Tor, I2P, not Tor, I2P or P2P, or I2P is what, I do P2P, oh, what do you call it, you're talking about VPN, right, I2P, going through VPN, what's I2P, these acronyms throw me off, I2P, I2P, the invisible internet project, no I haven't gotten there yet, is an enormous network layer that allows for censorship, resistant peer-to-peer communication, Bravo is a browser that offers that, yes, this sock is Bravo, one of the browsers that offers that thing, I2P, the one reason I haven't gone into this stuff is because of my hardware limitations right now, I need to upgrade, my main priority has been to create content, right, and I haven't tried to put any extra strain on the hardware that I've had to prevent me, you know, to hinder the progress that we have, to limit the progress that we have, right, one of the reasons is because I work my computers to the bone, right, one of my hard drives giving out is one of the examples, one of the things that happens, but as soon as I do a system upgrade, I'm going to dedicate Tor station, I'm going to look more into the invisible internet as well, you should take a look at the applied cryptography book by Schneer, I didn't mean to make that question, okay sure, this sock can you, if you're on Discord, if you could put this name of this book in our book folder, that way I'll know to look it up, and it's an archive, that way sometimes I go through those folders and I look up to see what people recommend it, and then I, because I can check out everything, but I use it in an archive and go in there and look up what, even music, what people have recommended, and I either grab the books which I have, I bought a couple books that people have recommended and whatnot, that'd be great, if you're not on Discord let me know and I'll try to keep in mind to make a note of this, oh one thing I was going to mention, you brought a cryptography that, we're how it cooked the currencies, cryptocurrencies, check this out, right, six months ago, six to a year ago, six months ago really, six months ago, six to eight months ago, Bitcoin was 50% of the market value of all cryptos, right, 50%, eight months ago, Bitcoin was 50% of the market cap of all the cryptos, and there's over 2,000 cryptos, right, I'll last that check, so 2,000 plus cryptocurrencies and Bitcoin had to hold on 50% of that market, right, right now Bitcoin holds 70% of the crypto market, that is a huge move, that is equivalent to what people are talking about, whenever you're talking about personal finance, investing in economics and stuff like this, you also have to consider the currency that you're in, right, so this is, it's an analogous to it, it's not exactly the same but it is analogous to it, right, so Bitcoin has seen an influx of 20% more of the market into it, relative to eight months ago, that could mean multiple things, right, but two of the things you can consider is this, either Bitcoin is overvalued and the other altcoins are undervalued and they're going to do a move soon to bring that ratio of Bitcoin to 50% again, you sort of have to look at the historic price of Bitcoin, this is why mathematics is brilliant, right, if you take a look at the averages of cryptocurrencies, let's assume crypto has been around, let's say 2009, 2008, 2008, 2009, let's say Bitcoin's been around, right, 2009, 10 I guess, so let's say 10 years, right, if over a 10 year period Bitcoin, initially for the first few years Bitcoin would have been 99% of the market, 100% of the market, right, and then Litecoin kicked in, whatnot, right, but let's assume in the last five years, Bitcoin was retaining 50% of the market share for alt cryptos, of all the cryptos, and right now it has 70% of market share, right, during the last few months, that's either a breakout and a complete readjustment of the market, like the basically the dot com burst in 1999, 1999, 2000, or it's foreshadowing what the alt coins are going to do, or the alt coins are foreshadowing what Bitcoin is going to do, which is what Bitcoin will come down to 50%, so there's so many different ways you're going to read this data, read this analysis, and if you know mathematics, if you know your stats, you can write programs or use programs or create graphs and charts and stuff like this to play the market according to if you're into that thing, I just like sometimes talking about why it's important to do certain things, why, how mathematics can be used for some of these things, and here's a kicker, the math, these drop in math through such as I put out, they get the, they're usually on the low end of how many years we get, right, but literally these are the most important streams that we do, because it's mathematics, it covers all the other things that we're doing, may it be politics, economics, comic books, cooking, whatever it even be, the foundation of these mathematics, right, brilliant, love it, by the way there's other people, a couple of people stopped to me recently that through Twitch that are actually doing live stream math tutoring sessions, and I'm so happy to see that, so I think if you start looking around on Twitch, if you need specific type of tutoring, math tutoring sessions, more frequent than what I'm doing, there's going to be people around that are doing math sessions as well, so look around, I haven't done any looking around, I've just noticed who's subbed to me that has started doing this, and love it, love it, love it, I'm so glad that people are offering this, well math is the universal language, 100% the universal language, right, the language that I use, use the most between humans and humans, humans and machines and machines and machines, and some people say no, it's not the most used between humans and humans, I go absolutely it is, there's a foundation, the language that's used, the common language that's used between all human beings, because when people are talking, I don't care what they're talking about, there's going to be numbers, percentages, stats, data, ratios in there somewhere, I love to do HS calculus, number theory, linear algebra streams like this, but I'm not good on the pressure or I can't, Mask of Raven, Lavia, you're doing it, welcome to a math stream, salutations, Mask of Raven, okay, check out my first off find it for you, well there's only one way to get over that, let me show you, let me show you, she told me, oh yeah I should just go over here, I'll go to my youtube channel and I'll grab you my first video that I put out when I put these videos together, created playlists, where is the language of mathematics, let's find the language of mathematics, where is my language of mathematics, you know, it's language of mathematics, it's the first playlist I created, oops I want to start it all off, I want to go to the playlist, you four playlists, this is the first video I ever put out where I was in front of the camera, you tell me, you tell me, this was, this was 2007, 2007, dude I was nervous, I just learned how to edit through, I was editing on a crappy little HP computer that I had that would never ever ever ever ever get again, an HP computer, it took me forever, I didn't know how to do lighting, camera, it was little V, VS, VH, HP tapes, little mini tapes I was taping on, no sound system, anything like this, brother if I can do it, anybody can do it, much darker beard, most definitely, 2007, 12 years ago, there's only one way to get over that, one way to get over that, I have to get back to work, have a good one, YouTube this song, thanks for popping by, thanks for popping by, alright, so that's my first math video, since then math video wise, we probably have like 300 plus math videos, over 700 plus videos, it feels good brother, really, it feels good sharing information, especially sharing things that I love being math-centric, okay, I can also tell you it's a good feeling, that it's well worth trying, you don't need to stick to it, we have 750 videos, it doesn't have to be everything you do or dominant force, but if you would like to do it, I would love to do HS calculus number three linear algebra streams like this, but I'm not good on the pressure or on camera, if you would love to do something like that, you only live once math, get it done, really, get it done, try it out, it's people are gonna call you out, people are gonna make fun of you, people are gonna laugh at what you do, they did to me, but at the same time, you get people that give you support, love what you're doing, thank you with gazillion times, I can't explain to you how many, I have no idea how many thank you messages I've received over the last 12 years of doing this, that is worth all the flak you might be getting and it actually, the flak you get gets you a little bit of thicker skin, gets you a little thicker skin and you start appreciating life a lot more, exactly, really, you start appreciating life a lot more because you're on a path that you love, like really, and there's something to be said about love being sent your way, mask of Raven, I kid you not, when you're down and everybody goes through ups and downs, when you're down, I can't even tell you how many times where I've had a rough day or a rough week or a rough month or a rough whatever it is and then all of a sudden someone sends me a message, like I read it and I'm like, wow, and then I go to my notes and figure out what I've laid out to do and I start doing like mass videos, yeah, yeah, yeah, it pumps you up, it pumps you up, it's amazing, I'll watch, I guess the second day of school starting people aren't really too much into doing math, we did some good math today man, we did some good math today, right, we did some great math there, should I tell you what, what do you call it, oh I don't have the spreadsheet here, do I have the spreadsheet here, no I don't have the spreadsheet here, it's on the other computer, I haven't loaded the spreadsheet on this one, so we can't crush the numbers alive, unfortunately, could you explain how to do synthetic polynomial division, I can do long division but I forget synthetic, yeah for sure, synthetic division, here check this out, synthetic division is just the shorter version of the long division, right, it's not a cheat but it's, here you can do polynomial long division like this, well I don't want to bother doing polynomial long division, let's just do for instance synthetic long division, right, let's assume you had this 5x to the power of 4 plus 7x cubed minus 2x plus 1, right, oh divide it by, let's keep it simple, let's just say x minus 3, no x minus 3, x plus 2, let's make this a 6, so you lay it out, if you're doing long division, this is the way you would lay it out, right, you would go x plus 2 and then you would go 5x to the power of 4 plus 7x cubed minus 2x plus 6, right, and then you go, what do you multiply x by to give you 5x to the power of 4, you lay it down, you go like this, right, which is legit, it's not, it's not bad, it's a good way to do it, sometimes I do it this way, right, if you do a synthetic long division, you do this, you say x plus 2 really means x plus 2 is equal to 0, which is x is equal to negative 2, so you're going to go x is equal to negative 2, you're going to remind, remember that this is x plus 2, okay, and then what you're going to do is you're going to take the coefficients in front of the variables and the constant term and just lay those out, forget about the x's or anything, the only thing you have to keep track of is these guys have to go sequentially down, so if this is x to the power of 4, that's x to the power of 3, we're missing x to the power of 2, so you're going to put a 0 as a place marker for x to the power of 2, so you're going to take the coefficients here, you're going to go 5, 7, x to the power of 2 is not there, so you're going to go 0 and then you remember that the sign in front of the number always goes with the number, so that's not a 2, that's a negative 2, negative 2 and then you're going to get a 0 and then what you do is this, that long division, you're going to bring this guy down 5, yeah, sometimes I like to look this up, right, and then you're going to go this times this and you're going to bring it here, so this guy goes here but it multiplies negative 2 on its way, so whatever was here you multiply, whatever's going up that way, right, so 5 times negative 2 is negative 10 and then you're going to add these guys, you're going to get negative 3, okay, and then you're going to take this, take it up there, multiply it by negative 2, you get 6, add it and you get 6, this guy goes there, multiplies negative 2, you get negative 12, add it and you get negative 14, this guy goes up, multiplies by negative 2, it comes to 28, right, and then you add them, you get 34, right, so what you ended up with is this, because you just took x to the power of 4 and divided out an x, I hope I did this right, okay, I have a just, I'm putting a disclaimer out there because 95% sure I did it right, but I'll put a disclaimer out there, if you go chicholong synthetic division you'll find a whole bunch of videos we've laid out, right, but basically what happens is, you add x to the power of 4, you took out an x, so this guy, these guys here are 5x cubed minus 3x squared plus 6x minus 14, this guy here is the remainder, and the remainder is what the y value would be if this was a function, if just this top guy was a function, if you plug in x is equal to negative 2, it would equal 34, so this is really a representation of a point on this function, this not included, when x is negative 2, y is 34, okay, that's what you're really finding, you're finding a point, and if that was 0 it would mean this is a factor of that, right, and we'll do a test to make sure we did this correctly, there's a way to do this is where they say, oh write down your division statement, your division statement will be this, this divided by this, oops 5x to the power of 4 plus 7x cubed minus 2x plus 6 divided by x plus oops 2 is equal to this plus 34 over x plus 2, and then if you multiply everything by x plus 2, what you end up getting is this, 5x to the power of 4 plus 7x cubed minus 2, what does it say, is equal to x plus 2 times 5x, because x plus 2 multiplies, everything is a common denominator in the whole equation, x cubed minus 3x squared plus 6x minus 14 plus 34, some people consider this to be the division statement, some people consider this to be the division statement, the meaning of this division is if you take x is equal to negative 2 and sub it into this function, then the remainder 34 is really a point on the function, right, that's what we've done, now if we want to do a check just to make sure we did this correctly, I can do this with a function that we know the factor of, so we could say, hey what's x squared plus 5x plus 6 divided by x plus 2, right, can you see that, hopefully, let's make this a little bit bigger, let's make this a little bit bigger, what we're doing, oh yeah, x, not just a power of 5x squared, x squared plus 5x plus 6 divided by x plus 2, and that's one thing I do in mathematics, if I want to make sure I did something complicated correctly, I use the same process for something simple that I know the answer of, right, so if we're doing this division, it means there's an imaginary one there, so and this means x equals negative 2, right, so you're going to go x is equal to negative 2, you're going to synthetically divide that into 1, 5, and 6, and x is equal to negative 2 means x plus 2, so we're seeing if x plus 2 is a factor of this, and when it's a factor of it, if the remainder is 0, it means that's where it crosses the x-axis, right, if this was 0, then when x was negative 2, this function would cross the x-intercept, right, so this becomes 1, 1 times negative 2 is negative 2, add them together, you get 3, 3 times negative 2 comes up here, becomes negative 6, so you get 0, the remainder is 0, which should be, which means if you take this function divided by x plus 2, then the remainder is 0, so it says this is an x-intercept, so if you plug in x is equal to negative 2 here, you get 0, f of x would be 0, the y would be 0, and the other factor would be x1, x plus 3, which it is, right, if you factor this guy, x squared plus 5x equals 6 is x plus 2 times x plus 3, you're done, right, you could write this as a division statement like this and like this and whatnot, right, you could take it from there, hopefully that was a good reminder for you, I tried to cover what you call it, cover some of the concept behind it, but we do have like a huge, huge series on that x, how are you doing, how is life, hope you're doing well, fun, you're catching us in the last few minutes of, of a math livestream, our first math livestream for the 2019-2020 school, I wonder how many we'll get done this year, I definitely want to do a marathon session, drop in math tutoring marathon session, by that time hopefully, do an exam time anyway, by that time hopefully I'll set something up and we'll get a gigantic board and maybe we'll do, we'll try to break our record of the longest livestream we've done, we did a six, six and a half hour making crab apple livestream, right, I think six and a half hours, maybe we'll set enough for a seven hour math drop-in tutoring session or an eight hour one, by that time my voice might give away though, after eight hours in will, I can't do eight hours of talking but maybe we'll figure something out, maybe we'll play some old videos and then we'll do it live and then ask questions, that'd be great actually, today for these four hours we're going to go through series one of the language of mathematics, adding, subtracting, multiplying, dividing and then we'll kick it out into series two exponents and radicals dealing with fractions, prime factorization, those are series one actually, dealing with radicals exponents with series two, functions, graphs and stuff with series three A and B, ratios, there's four, that'd be fun, that'd be fun, am I going to have time, I won't have time to go pick up my comic books today or tomorrow, oh no, oh no, I might be missing out on something large, what, I might be missing out on this note, but it's worth it, for mathematics we'll skip a Wednesday of picking up comic books, yeah, I think so, I think so, for mathematics we're willing to do a few things, should we call it a stream game, this was good, this was a good way to break things in, a little bit less than two hours but that's okay, I got some blackberries to mill and jar and I got a whole bunch of shish kebabs to make, if I get into it, no, we're not gonna do, I'm not gonna do a non-live stream there, to make the shish kebabs, I gotta do further prep and organize things and stuff, we're doing our first legit barbecue tomorrow with a whole bunch of friends coming over, I'm gonna feed them Armenian Persian style of chicken kebabs and beef ground beef kebabs, a candler stuff, not a candler, if you speak Farsi, juje kebabs are kubide, kubide is ground shish kebabs or ground kebabs and chicken, juje means chicken, can wait, can wait, I hope you guys are having a fantastic Wednesday, I hope you guys continue to have a fantastic Wednesday, mask of raven, thank you very much for the questions and interaction, that was fun, this skalk is gone, thank you for the questions that you had, Livia, thank you for popping in, KC was here for a bit and trepid, never been a negative, sneaky walrus or spice power, there's ra, lions, these chill low view streams are pretty nice and relaxing, we don't get troll action and everything, fantastic, okay, I hope you have a fantastic next few days, I don't think I'm gonna be setting up any live streams until next, not this weekend, the following weekend, so it's gonna be about a 10 day break, I got students to deal with, gonna have to watch the video, have a good one, should show you two acts, lots of love Livia, lots of love, hope you have a fantastic evening, taco, how are you doing, we're just about to end the stream, we did some nice mathematics and we watched some comic books sell on, well not watched but tracked some of the comic books that we did, we sold all the first carnage appearances of Amazing Spider-Man, very cool, very cool, very cool, important books, beautiful books, beautiful books, so in about, I assume by Monday we'll have our next schedule up for the following weekend and the odds are we'll probably do now, so what day are we, what days are gonna be, probably next streams are gonna be, maybe starting September 13th or 14th, sorry for the long delay but it just has to be, it just has to be, I might try to do one or two, maybe one random all weekend, I'll see, I'll see what I want to, aside from that thanks for being here again, I hope you have a fantastic next few days, bye for now